What is 0 best location in the real number system

Identify the slope of the line that passes through the given points <br><br> (5,2) and (-4,6)

Naya [18.7K]

Answer:

-4/9

Step-by-step explanation:

Slope is rise over run, or change in y over change in x.

We get: (6-2)/(-4-5)=4/-9 or -4/9

4 0

3 years ago

The basketball shown is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of

Nadya [2.5K]

Answer:

See example below.

Step-by-step explanation:

The volume of a ball is found using the formula V = 4/3πr³. In this example, you know the volume is 4500π. Substitute V = 4500π and solve for r.

4500π = 4/3πr³

4500 = 4/3r³

3375 = r³

15 = r

This means the diameter of the ball is 30.

Since the box had the same side length as the diameter, this means the volume of the box is V = 30*30*30 = 27,000.

5 0

4 years ago

Triangles R S T and V U T are connected at point T. Angles R S T and V U T are right angles. The length of side R S is 12 and th

kkurt [141]

Answer:

$\dfrac{\overline{RS}}{\overline{VU}}=\dfrac{\overline{ST}}{\overline{UT}}\quad\text{and}\quad\angle S\cong\angle U$

Step-by-step explanation:

To use the SAS similarity theorem, you must show proportionality between corresponding sides, and congruence of the angle between them.

The answer shown above is the only answer choice that mentions an angle.

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<em>Comment on other choices</em>

Choice B shows the three sides are proportional, so would be useful if the SSS similarity theorem were to be invoked. It isn't helpful for the using the SAS similarity theorem.

Choices C and D get the proportion statements wrong.

6 0

3 years ago

Read 2 more answers

Test the claim that the mean GPA of night students is larger than 2 at the .025 significance level. The null and alternative hyp

exis [7]

Answer:

$H_0: \, \mu = 2$ .

$H_1:\, \mu > 2$ .

Test statistics: $z \approx 2.582$ .

Critical value: $z_{1 - 0.025} \approx 1.960$ .

Conclusion: reject the null hypothesis.

Step-by-step explanation:

The claim is that the mean $\mu$ is greater than $2$ . This claim should be reflected in the alternative hypothesis:

$H_1:\, \mu > 2$ .

The corresponding null hypothesis would be:

$H_0:\, \mu = 2$ .

In this setup, the null hypothesis $H_0:\, \mu = 2$ suggests that $\mu_0 = 2$ should be the true population mean of GPA.

However, the alternative hypothesis $H_1:\, \mu > 2$ does not agree; this hypothesis suggests that the real population mean should be greater than $\mu_0= 2$ .

One way to test this pair of hypotheses is to sample the population. Assume that the population mean is indeed $\mu_0 = 2$ (i.e., the null hypothesis is true.) How likely would the sample (sample mean $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ ) be observed in this hypothetical population?

Let $\sigma$ denote the population standard deviation.

Given the large sample size $n = 60$ , the population standard deviation should be approximately equal to that of the sample:

$\sigma \approx s = 0.06$ .

Also because of the large sample size, the central limit theorem implies that $Z= \displaystyle \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}}$ should be close to a standard normal random variable. Use a $Z$ -test.

Given the observation of $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ :

$\begin{aligned}z_\text{observed}&= \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}} \\ &\approx \frac{\overline{X} - \mu_0}{s / \sqrt{n}} = \frac{2.02 - 2}{0.06 / \sqrt{60}} \approx 2.582\end{aligned}$ .

Because the alternative hypothesis suggests that the population mean is greater than $\mu_0 = 2$ , the null hypothesis should be rejected only if the sample mean is too big- not too small. Apply a one-sided right-tailed $z$ -test. The question requested a significant level of $0.025$ . Therefore, the critical value $z_{1 - 0.025}$ should ensure that $P( Z > z_{1 - 0.025}) = 0.025$ .

Look up an inverse $Z$ table. The $z_{1 - 0.025}$ that meets this requirement is $z_{1 - 0.025} \approx 1.960$ .

The $z$ -value observed from the sample is $z_\text{observed}\approx 2.582$ , which is greater than the critical value. In other words, the deviation of the sample from the mean in the null hypothesis is sufficient large, such that the null hypothesis needs to be rejected at this $0.025$ confidence level in favor of the alternative hypothesis.

3 0

3 years ago

Help me and ill give you brainliest thanks

notsponge [240]

Yes, it is a rectangle the slope of ab is 1/5 the slope of cues it is a rectangle the slope of ab is 1/5 the slope of cd is also 1/5 the slope of bc is -1/6 so is da

4 0

3 years ago